recent ccc progress in atomic and molecular collision theory · 2020. 2. 28. · and molecular...

Introduction

Convergent close-coupling theory

Recent applications of CCC

Recent CCC progress in atomic and

molecular collision theory

I. Abdurakhmanov, J. Bailey, A. Bray∗, I. Bray, D. Fursa,

A. Kadyrov, C. Rawlins, J. Savage, and M. Zammit†

Curtin University, Perth, Western Australia∗Research School of Physics and Engineering, ANU

†Theoretical Division, Los Alamos National Laboratory, USA

Vapour Shielding CRP, IAEA, Vienna, Mar., 2019

Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction




Introduction



Outline

1 Introduction

2 Convergent close-coupling theory

target structure and scattering

new approach to solving CCC equations

internal consistency

3 Recent applications of CCC

antihydrogen formation

positron and electron scattering on molecular hydrogen

heavy projectiles


Introduction



MotivationIntroduction

The primary motivation is to provide accurate atomicand molecular collision data for science and industry

Astrophysics

Fusion research

Lighting industry

Neutral antimatter formation

Medical: cancer imaging and therapy

Provide a rigorous foundation for collision theory with

long-ranged (Coulomb) potentials.


Introduction



ChallengesIntroduction

Collisions between particles on the atomc scale are

difficult to calculate:

Governed by the Laws of Quantum Mechanics

Charged particles interact at large distances

Countably infinite discrete spectrum

Uncountably infinite target continuum

Can be multicentred (charge exchange, Ps-formation)


Introduction



History: computationalIntroduction

Prior to the 1990s theory and experiment generallydid not agree for:

electron-hydrogen excitation or ionization,

electron-helium excitation or (single) ionization,

single or double photoionization of helium.

The convergent close-coupling (CCC) theory for

electron, positron, photon, (anti)proton collisions with

atoms or molecules is applicable at all energies for

the major excitation and ionization processes.


Introduction



History: formal theoryIntroduction

Prior to 2008, no satisfactory mathematicalformulation in the case of long-ranged (Coulomb)potentials for positive-energy scattering in

Two-body problems,

Three-body problems.

Surface integral approach to scattering theory is validfor short- and long-ranged potentials:

Kadyrov et al. Phys. Rev. Lett., 101, 230405 (2008),

Kadyrov et al. Annals of Physics, 324, 1516 (2009),

Bray et al. Physics Reports, 520, 135 (2012).


Introduction






Convergent close-coupling theorytarget structure

For complete Laguerre basis ξ(λ)nl (r), target states:

“one-electron” (H, Ps, Li,. . . ,Cs, H+2 )

φ(λ)nl (r) =

Nl∑

n′=1

Cn′

nl ξ(λ)n′l (r),

“two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H2, H2O)

φ(λ)nls (r1, r2) =

∑

n′,n′′

Cn′n′′

nls ξ(λ)n′l ′(r1)ξ

(λ)n′′l ′′(r2),

Diagonalise the target (FCHF) Hamiltonian

〈φ(λ)f |HT|φ

(λ)i 〉 = ε

(λ)f δfi .


Introduction






e+-H energies for NℓH= Nℓ

Ps= 12 − ℓ, for ℓ ≤ 3

0.1

1

10

100

1000

H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F)

-0.01

-0.1

-1

-10

-100H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F)

Energy levels (eV)


Introduction







Use complete sets of states to isolate

GLn(r

′, r ′′) =∑

∫

dkfL(kr ′)fL(kr ′′)

E + i0 − ǫn − εk

= −π

kn

fL(knr<) (gL(knr>) + i fL(knr>)) . (3)

Eq. (2) becomes [A. Bray et al. CPC 212 55 (2017)]

〈k fφf |T |φik i〉 = 〈k fφf |V |φik i〉

+

NT+NPs∑

n=1

∫

d3k〈k fφf |V′|φnk〉〈kφn|T |φik i〉. (4)

Works for kf = 0 for neutral and ionic targets.


Introduction






e-He+ 2s and 2p excitation

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

0.0400

10-4 10-3 10-2 10-1 10+0 10+1 10+2

cross section (a.u.)

→

singlet 2s

nGF aGF

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

10-4 10-3 10-2 10-1 10+0 10+1 10+2

→

triplet 2s

nGF aGF

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

0.0600

10-4 10-3 10-2 10-1 10+0 10+1 10+2


electron energy above threshold (eV)

→

2p nGF aGF

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

10-4 10-3 10-2 10-1 10+0 10+1 10+2

→

2p nGF aGF


Introduction






Helium single and double photoionisation

0

1

2

3

4

5

6

7

8

10-4

10-3

10-2

10-1

10+0

10+1

10+2

10+3

→

σ1 Samson

nGF

aGF 0.00

0.03

0.06

0.09

0.12

0.15

0.18

10-4

10-3

10-2

10-1

10+0

10+1

10+2

10+3

→

σ2 nGF

aGF

Wehlitz

0.00

0.01

0.02

0.03

10-4

10-3

10-2

10-1

10+0

10+1

10+2

10+3

cross section (Mb)

photoelectron energy above threshold (eV)

→

σ3 nGF

aGF

Wehlitz0.000

0.002

0.004

0.006

0.008

0.010

10+0

10+1

10+2

10+3

σ2+

nGF

aGF

Doerner

[A. Bray, A. Kheifets, I. Bray, PRA 95, 053405 (2017)]

[A. Kheifets, A. Bray, I. Bray, PRL 117, 143202 (2016)]


Introduction







In positron scattering there are two centres:1 target: discrete and continuous spectrum2 positronium: discrete and continuous spectrum

One-centre complete expansion:

Ps-formation is within ionization σ(1)ion

: e-loss

boundary condition problem in the extended Ore gap

Two-centre complete expansion:

explicit Ps-formation σ(2)Ps

and breakup σ(2)brk

: e-loss

ill-conditioned, but no double counting

Internal consistency:

above ionization threshold: σ(1)ion

= σ(2)Ps

+ σ(2)brk

below Ps-formation threshold: σ(1)ii = σ

(2)ii


Introduction






one- and two-centre positron-hydrogen calculations

N N N Ps

NNPs

ε=0 ε=0 ε=0

ε=0

Nε=0

ε=0

H

H

H

i i

f f

σfi

(2)σfi

(1) H(1) (2) (2)

(2)

(2)

(1)


Introduction






e+-H(1s) calculated with CCC(NH

lmax,NPs

lmax) for L = 0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100

cross section (

π a02)

projectile energy (eV)

totalCCC(309, 0)CCC(202,202)

0.00

0.01

0.02

0.03

0.04

0 20 40 60 80 100

Ps(continuum)

Ps(bound)

electron loss

[Bailey et al. Phys. Rev. A 91, 012712 (2015)]


Introduction





heavy projectiles


Ps(n ≤ 3) + p̄ → H̄ + e−

100

101

102

103

104

105

106

107

108

10-5 10-4 10-3 10-2 10-1 100 101

cros

s se

ctio

n (a

.u.)

Ps energy ε (eV)

(anti)hydrogen formation CCC Ps(1s) CCC Ps(2s) CCC Ps(2p) CCC Ps(3s) CCC Ps(3p) CCC Ps(3d) UBA Ps(2s) UBA Ps(2p) UBA Ps(1s) Variational Ps(1s) Merrison 1997

[Kadyrov et al. Phys. Rev. Lett. 114, 183201 (2015)]


Introduction





heavy projectiles


Ps(n ≤ 5) + p̄ → H̄ + e−

100

101

102

103

104

105

106

107

108

109

10-5 10-4 10-3 10-2 10-1 10+0


Ps(n) energy(eV)

antiH formationPs(n

i = 1)

Ps(ni = 2)

Ps(ni = 3)

Ps(ni = 4)

Ps(ni = 5)

[Kadyrov et al. Nature Communications 8, 1544 (2017)]


Introduction





heavy projectiles

antihydrogen formation and elastic scattering

Ps(1s)+p̄ →

{

H̄(1s) + e−

Ps(1s) + p̄

10-2

10-1

100

101

102

103

104

10-5 10-4 10-3 10-2 10-1 10+0


Ps(1s) energy (eV)

L=0

Ps(1s)+p TT Ps(1s) H(1s)

[Fabrikant et al. Phys. Rev. A 94, 012701 (2016)]


Introduction





heavy projectiles

antihydrogen formation and elastic scattering

Ps(2s)+p̄ →

{

H̄(2s) + e−

Ps(2s) + p̄

100

101

102

103

104

105

106

107

10-5 10-4 10-3 10-2 10-1 10+0


Ps(2s) energy (eV)

L=0

Ps(2s)+p TT Ps(2s) H(2s)

[Fabrikant et al. Phys. Rev. A 94, 012701 (2016)]


Introduction





heavy projectiles

positron scattering on molecular hydrogen

e+-H2 collisions: total cross section

1

10

100

0.1 1 10 100 1000

Cro

ss S

ection (

units o

f a

02)

Incident Energy (units of eV)

GTCS X1 Σg

CCC lmax=8 N=556

Hoffman et al.Machacek et al. ang. corrected

Machacek et al.Charlton et al.Karwasz et al.

Zecca et al.

[Zammit et al. Phys. Rev. A 87, 020701 (2013)]


Introduction





heavy projectiles


e+-H2 collisions: internal consistency

0

2

4

6

8

10

12

14

16

18

20

10 100 1000

cross

sec

tio

n (

a.u.)

incident energy (eV)

GTCS

CCC(142,21)

CCC(108,0)

Machacek et al.

Hoffman et al.

Charlton et al.

Karwasz et al.

Zecca et al.

0

2

4

6

8

10

12

10 100 1000cr

oss

sec

tio

n (

a.u.)


electron-loss CCC(142,21)

CCC(108,0)

Moxom et al.

Fromme et al.

[Utamuratov et al. Phys. Rev. A 92, 032707 (2015)]


Introduction





heavy projectiles


e+-H2 collisions: Ps-formation

0

2

4

6

8

10

10 100

cro

ss s

ecti

on

(in

a.u

.)


Ps-formationCCC(141,1)

CCC(141,3)

CCC(142,3)

Biswas et al.

Zhou et al.

Fromme et al.

Machacek et al.

[Utamuratov et al. Phys. Rev. A 92, 032707 (2015)]


Introduction





heavy projectiles

electron scattering on molecular hydrogen

e−-H2 collisions: total cross section

1

10

100

0.1 1 10 100

Cro

ss S

ection (

units o

f a

02)

Incident Energy (eV)

CCCFerch et al.van Wingerden et al.Hoffman et al.Deuring et al.JonesSubramanian and KumarNickel et al.Zhou et al.

[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction





heavy projectiles


e−-H2 collisions: total ionization

0

1

2

3

4

50 100 150 200 250 300

Cro

ss S

ection (

units o

f a

02)

Incident Energy (eV)

CCCRMPS Gorfinkiel and TennysonTDCC Pindzola et al.Rapp and Englander-GoldenKrishnakumar and SrivastavaStraub et al.Lindsay and Mangan

[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction





heavy projectiles


e−-H2 collisions: b3Σ+u excitation

0.0

0.5

1.0

1.5

2.0

2.5

3.0

10 15 20 25

cros

s se

ctio

n (a

.u.)


b 3Σu+

Nishimura and Danjo (1986) Khakoo and Segura (1994) MCCC (2017) experiment (2018)

[Zawadski et al. PRA 98, 050702R (2018)]


Introduction





heavy projectiles

proton scattering on hydrogen

p+-H collisions: internal consistency

0.0

2.0

4.0

6.0

8.0

10.0

101

102

103

cro

ss s

ecti

on

(1

0-1

6 c

m2)

projectile energy (keV)

experiment: e-loss QM-CCC(508, 0): e-loss QM-CCC: e-loss QM-CCC: ionization QM-CCC: e-capture

[Abdurakhmanov et al. J. Phys. B 49, 115203 (2016)]Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction





heavy projectiles

proton scattering on hydrogen

p+-H collisions: capture and ionization

10-5

10-4

10-3

10-2

10-1

100

101

101

102

103

cross

sec

tion (

10

-16 c

m2)


electron capture

Winter Kolakowska QM-CCC

10-5

10-4

10-3

10-2

10-1

100

101

101

102

103

cross

sec

tion (

10

-16 c

m2)


McClure Bayfield Wittkower Hvelplund

0.0

0.5

1.0

1.5

2.0

101

102

103

cross

sec

tion (

10

-16 c

m2)


ionization

Toshima Winter Sidky Ovchinnikov Kolakowska QM-CCC

0.0

0.5

1.0

1.5

2.0

101

102

103

cross

sec

tion (

10

-16 c

m2)


Shah 81 Shah 87 Kerby 95

[Abdurakhmanov et al. J. Phys. B 49, 115203 (2016)]


Introduction





heavy projectiles

antiproton scattering on molecular hydrogen

p−-H2 collisions: total ionization

0.0

0.5

1.0

1.5

2.0

2.5

1 10 100 1000

cro

ss s

ecti

on

(1

0-1

6 c

m2)


Lu..

hr I Lu

..hr II

Lee I Lee II Ermolaev CCC

0.0

0.5

1.0

1.5

2.0

2.5

1 10 100 1000

cro

ss s

ecti

on

(1

0-1

6 c

m2)


Knudsen Hvelplund Andersen

[Abdurakhmanov et al. PRL 111, 173201 (2013)]Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction





heavy projectiles

antiproton scattering on molecular hydrogen

p−-H2 collisions: comparison with H and He

0.0

0.5

1.0

1.5

2.0

0.2 0.4 0.6 0.8 1

cro

ss s

ecti

on

(1

0-1

6 c

m2)

projectile velocity (a.u.)

Knudsen: H Hvelplund: He Knudsen: He Hvelplund: H2 Knudsen: H2

H

H2

He

[Abdurakhmanov et al. PRL 111, 173201 (2013)]Igor Bray <[email protected]> Recent CCC progress in atomic and molecular collision theory

Introduction





heavy projectiles

Concluding remarks

CCC method has been implemented for scattering of

electrons, positrons, photons, protons and

antiprotons on quasi one- and two-electron targets,

as well as inert gases.

Two-center problems have self-consistency checks

To-do list

Ps-H, Ps-He+, Ps-H+2

Ps-Ne+, and other inert gas ions

H-He+, H-H+2 , H-Ne+, and other inert gas ions

X2, H2O and other molecular targets


recent ccc progress in atomic and molecular collision theory · 2020. 2. 28. · and molecular...

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